Finite Group Databasebeta

← C127×#8407 #44572080

Subgroups — C127×#8407 #44572080

Order 32512.

900 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#539×C127C211yesmaximal, characteristic
2C127×#1874C211yesmaximal, characteristic
3C127×#1872C211yesmaximal, characteristic, complemented
4C2×#328×C127C211yesmaximal, characteristic, complemented
5C2×#327×C127C211yesmaximal, characteristic
6C2×#324×C127C211yesmaximal, characteristic, complemented
7C127×#1441C211yesmaximal, characteristic, complemented
8#539×C127—22no—
9#539×C127—22no—
10#539×C127—22no—
11#539×C127C414yescomplemented
12C2×#126×C127—21no—
13C2×#125×C127—21no—
14C2×#123×C127—21no—
15C2×#123×C127—21no—
16C2×C22⋊Q8×C127—21no—
17C2×C22⋊Q8×C127C2211yescharacteristic
18C2×#121×C127C2211yescharacteristic
19C2×C4×D4×C127—21no—
20C22×C4⋊C4×C127C2211yescharacteristic
21C22×C4⋊C4×C127C2211yescharacteristic
22C2×#103×C127—21no—
23C2×#102×C127—21no—
24C2×C22⋊C8×C127C2211yescharacteristic
25C2×C22⋊C8×C127C2211yescharacteristic
26C2×#95×C127—21no—
27C2×#95×C127—21no—
28C2×#95×C127C2211yescharacteristic
29#340×C127—21no—
30#340×C127—21no—
31#328×C127—22no—
32#327×C127—22no—
33#324×C127—22no—
34C22×Q8×C127D411yescharacteristic
35C22×D4×C127—21no—
36C22×D4×C127D411yescharacteristic
37C23×C4×C127—21no—
38C23×C4×C127—21no—
39C23×C4×C127—21no—
40C23×C4×C127D411yescharacteristic
41C23×C4×C127D411yescharacteristic
42C23×C4×C127C2311yescharacteristic
43C22×C8×C127—21no—
44C22×C8×C127—21no—
45#126×C127—24no—
46#126×C127—24no—
47#125×C127—24no—
48#125×C127—24no—
49#123×C127—24no—
50#123×C127—24no—
51#123×C127—24no—
52#123×C127—24no—
53C22⋊Q8×C127—24no—
54C22⋊Q8×C127—24no—
55C22⋊Q8×C127—21no—
56C22⋊Q8×C127—21no—
57C22⋊Q8×C127C2×C412yes—
58C22⋊Q8×C127D412yes—
59#121×C127—21no—
60#121×C127—21no—
61#121×C127C2×C412yes—
62#121×C127D412yes—
63C4×D4×C127—24no—
64C4×D4×C127—24no—
65C2×C4⋊C4×C127—21no—
66C2×C4⋊C4×C127—21no—
67C2×C4⋊C4×C127—21no—
68C2×C4⋊C4×C127—21no—
69C2×C4⋊C4×C127—21no—
70C2×C4⋊C4×C127—21no—
71C2×C4⋊C4×C127—21no—
72C2×C4⋊C4×C127—21no—
73C2×C4⋊C4×C127—21no—
74C2×C4⋊C4×C127—21no—
75C2×C4⋊C4×C127—42no—
76C2×C4⋊C4×C127C2×C412yes—
77C2×C4⋊C4×C127D412yes—
78C2×C4⋊C4×C127D411yescharacteristic
79C2×C4⋊C4×C127D411yescharacteristic
80C2×C22⋊C4×C127—21no—
81C2×C22⋊C4×C127—21no—
82C2×C22⋊C4×C127—21no—
83C2×C22⋊C4×C127—21no—
84C2×C22⋊C4×C127—21no—
85C2×C42×C127—21no—
86#103×C127—42no—
87#102×C127—42no—
88C22⋊C8×C127—21no—
89C22⋊C8×C127—21no—
90C22⋊C8×C127—21no—
91C22⋊C8×C127—21no—
92#95×C127—21no—
93#95×C127—21no—
94#95×C127—42no—
95#95×C127—42no—
96C24×C127—21no—
97C24×C127C2×D411yescharacteristic
98C2×Q8×C127—21no—
99C2×Q8×C127—41no—
100C2×Q8×C127—41no—
101C2×Q8×C127C22⋊C412yes—
102C2×D4×C127—22no—
103C2×D4×C127—22no—
104C2×D4×C127—21no—
105C2×D4×C127—41no—
106C2×D4×C127—41no—
107C2×D4×C127—41no—
108C2×D4×C127—41no—
109C2×D4×C127—41no—
110C2×D4×C127—41no—
111C2×D4×C127C22⋊C412yes—
112C22×C4×C127—21no—
113C22×C4×C127—21no—
114C22×C4×C127—21no—
115C22×C4×C127—21no—
116C22×C4×C127—21no—
117C22×C4×C127—21no—
118C22×C4×C127—21no—
119C22×C4×C127—21no—
120C22×C4×C127—21no—
121C22×C4×C127—21no—
122C22×C4×C127—24no—
123C22×C4×C127—21no—
124C22×C4×C127—22no—
125C22×C4×C127—22no—
126C22×C4×C127—41no—
127C22×C4×C127—41no—
128C22×C4×C127—41no—
129C22×C4×C127—41no—
130C22×C4×C127—41no—
131C22×C4×C127—41no—
132C22×C4×C127—41no—
133C22×C4×C127—41no—
134C22×C4×C127—41no—
135C22×C4×C127—41no—
136C22×C4×C127—41no—
137C22×C4×C127—41no—
138C22×C4×C127—41no—
139C22×C4×C127—41no—
140C22×C4×C127—41no—
141C22×C4×C127—41no—
142C22×C4×C127—81no—
143C22×C4×C127—81no—
144C22×C4×C127C22⋊C412yes—
145C22×C4×C127C22⋊C412yes—
146C22×C4×C127C22×C411yescharacteristic
147C22×C4×C127C2×D411yescharacteristic
148C22×C4×C127C2×D411yescharacteristic
149C22×C4×C127C2×D411yescharacteristic
150C22×C4×C127C2×D411yescharacteristic
151C22×C4×C127C2×D411yescharacteristic
152C2×C8×C127—41no—
153C2×C8×C127—41no—
154C2×C8×C127—41no—
155C2×C8×C127—41no—
156C2×C8×C127—41no—
157C2×C8×C127—41no—
158C4⋊C4×C127—24no—
159C4⋊C4×C127—24no—
160C4⋊C4×C127—24no—
161C4⋊C4×C127—22no—
162C4⋊C4×C127—22no—
163C4⋊C4×C127—22no—
164C4⋊C4×C127—22no—
165C4⋊C4×C127—22no—
166C4⋊C4×C127—22no—
167C4⋊C4×C127—21no—
168C4⋊C4×C127—21no—
169C4⋊C4×C127—22no—
170C4⋊C4×C127—22no—
171C4⋊C4×C127—41no—
172C4⋊C4×C127—41no—
173C4⋊C4×C127C22⋊C412yes—
174C4⋊C4×C127C22⋊C412yes—
175C22⋊C4×C127—24no—
176C22⋊C4×C127—24no—
177C22⋊C4×C127—24no—
178C22⋊C4×C127—22no—
179C22⋊C4×C127—22no—
180C22⋊C4×C127—22no—
181C22⋊C4×C127—22no—
182C42×C127—24no—
183C23×C127—21no—
184C23×C127—21no—
185C23×C127—21no—
186C23×C127—21no—
187C23×C127—22no—
188C23×C127—41no—
189C23×C127—41no—
190C23×C127—41no—
191C23×C127—41no—
192C23×C127—41no—
193C23×C127—41no—
194C23×C127C2×C22⋊C411yescharacteristic
195C23×C127#12011yescharacteristic
196C23×C127#12011yescharacteristic
197C23×C127#13511yescharacteristic
198C23×C127#13511yescharacteristic
199C23×C127AGL(1,ℤ/8)11yescharacteristic
200C23×C127#13711yescharacteristic
201Q8×C127—42no—
202Q8×C127—81no—
203D4×C127—42no—
204D4×C127—42no—
205D4×C127—42no—
206D4×C127—42no—
207D4×C127—42no—
208D4×C127—81no—
209C2×C4×C127—21no—
210C2×C4×C127—21no—
211C2×C4×C127—21no—
212C2×C4×C127—21no—
213C2×C4×C127—22no—
214C2×C4×C127—22no—
215C2×C4×C127—22no—
216C2×C4×C127—22no—
217C2×C4×C127—22no—
218C2×C4×C127—22no—
219C2×C4×C127—22no—
220C2×C4×C127—41no—
221C2×C4×C127—41no—
222C2×C4×C127—41no—
223C2×C4×C127—41no—
224C2×C4×C127—41no—
225C2×C4×C127—41no—
226C2×C4×C127—41no—
227C2×C4×C127—41no—
228C2×C4×C127—41no—
229C2×C4×C127—41no—
230C2×C4×C127—41no—
231C2×C4×C127—41no—
232C2×C4×C127—41no—
233C2×C4×C127—41no—
234C2×C4×C127—41no—
235C2×C4×C127—41no—
236C2×C4×C127—42no—
237C2×C4×C127—42no—
238C2×C4×C127—42no—
239C2×C4×C127—42no—
240C2×C4×C127—42no—
241C2×C4×C127—42no—
242C2×C4×C127—42no—
243C2×C4×C127—81no—
244C2×C4×C127—84no—
245C2×C4×C127—81no—
246C2×C4×C127—81no—
247C2×C4×C127—81no—
248C2×C4×C127—81no—
249C2×C4×C127—81no—
250C2×C4×C127—81no—
251C2×C4×C127—81no—
252C2×C4×C127—81no—
253C2×C4×C127C2×C22⋊C411yescharacteristic
254C2×C4×C127C2×C22⋊C411yescharacteristic
255C2×C4×C127#12011yescharacteristic
256C2×C4×C127#12011yescharacteristic
257C8×C127—81no—
258C8×C127—81no—
259C22×C127—21no—
260C22×C127—21no—
261C22×C127—21no—
262C22×C127—21no—
263C22×C127—21no—
264C22×C127—21no—
265C22×C127—21no—
266C22×C127—21no—
267C22×C127—21no—
268C22×C127—21no—
269C22×C127—21no—
270C22×C127—21no—
271C22×C127—42no—
272C22×C127—42no—
273C22×C127—42no—
274C22×C127—81no—
275C22×C127—81no—
276C22×C127—81no—
277C22×C127—81no—
278C22×C127#37911yescharacteristic
279C22×C127#41611yescharacteristic
280C22×C127#41711yescharacteristic
281C22×C127#44911yescharacteristic
282C22×C127#44911yescharacteristic
283C22×C127#45211yescharacteristic
284C22×C127#45211yescharacteristic
285C22×C127#45411yescharacteristic
286C22×C127#45611yescharacteristic
287C22×C127B(4,𝔽2)11yescharacteristic
288C22×C127#45811yescharacteristic
289C4×C127—21no—
290C4×C127—21no—
291C4×C127—21no—
292C4×C127—21no—
293C4×C127—42no—
294C4×C127—42no—
295C4×C127—42no—
296C4×C127—42no—
297C4×C127—42no—
298C4×C127—82no—
299C4×C127—82no—
300#8407C12711yesmaximal, characteristic, direct product factor, Sylow
301C2×C127—21no—
302C2×C127—21no—
303C2×C127—21no—
304C2×C127—21no—
305C2×C127—82no—
306C2×C127#159711yescharacteristic
307C2×C127#160311yescharacteristic
308C2×C127#160911yescharacteristic
309C2×C127#161511yescharacteristic
310C2×C127#178811yescharacteristic
311C2×C127#179011yescharacteristic
312C2×C127#179311yescharacteristic
313C2×#539C2×C12711yescharacteristic
314#1874C2×C12711yescharacteristic
315#1872C2×C12711yescharacteristic, complemented
316C2×#328C2×C12711yescharacteristic, complemented
317C2×#327C2×C12711yescharacteristic
318C2×#324C2×C12711yescharacteristic, complemented
319#1441C2×C12711yescharacteristic, complemented
320C127#840711yescharacteristic, direct product factor, Sylow
321#539—22no—
322#539—22no—
323#539—22no—
324#539C4×C12714yescomplemented
325C2×#126—21no—
326C2×#125—21no—
327C2×#123—21no—
328C2×#123—21no—
329C2×C22⋊Q8—21no—
330C2×C22⋊Q8C22×C12711yescharacteristic
331C2×#121C22×C12711yescharacteristic
332C2×C4×D4—21no—
333C22×C4⋊C4C22×C12711yescharacteristic
334C22×C4⋊C4C22×C12711yescharacteristic
335C2×#103—21no—
336C2×#102—21no—
337C2×C22⋊C8C22×C12711yescharacteristic
338C2×C22⋊C8C22×C12711yescharacteristic
339C2×#95—21no—
340C2×#95—21no—
341C2×#95C22×C12711yescharacteristic
342#340—21no—
343#340—21no—
344#328—22no—
345#327—22no—
346#324—22no—
347C22×Q8D4×C12711yescharacteristic
348C22×D4—21no—
349C22×D4D4×C12711yescharacteristic
350C23×C4—21no—
351C23×C4—21no—
352C23×C4—21no—
353C23×C4D4×C12711yescharacteristic
354C23×C4D4×C12711yescharacteristic
355C23×C4C23×C12711yescharacteristic
356C22×C8—21no—
357C22×C8—21no—
358#126—24no—
359#126—24no—
360#125—24no—
361#125—24no—
362#123—24no—
363#123—24no—
364#123—24no—
365#123—24no—
366C22⋊Q8—24no—
367C22⋊Q8—24no—
368C22⋊Q8—21no—
369C22⋊Q8—21no—
370C22⋊Q8C2×C4×C12712yes—
371C22⋊Q8D4×C12712yes—
372#121—21no—
373#121—21no—
374#121C2×C4×C12712yes—
375#121D4×C12712yes—
376C4×D4—24no—
377C4×D4—24no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—42no—
389C2×C4⋊C4C2×C4×C12712yes—
390C2×C4⋊C4D4×C12712yes—
391C2×C4⋊C4D4×C12711yescharacteristic
392C2×C4⋊C4D4×C12711yescharacteristic
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C42—21no—
399#103—42no—
400#102—42no—
401C22⋊C8—21no—
402C22⋊C8—21no—
403C22⋊C8—21no—
404C22⋊C8—21no—
405#95—21no—
406#95—21no—
407#95—42no—
408#95—42no—
409C24—21no—
410C24C2×D4×C12711yescharacteristic
411C2×Q8—21no—
412C2×Q8—41no—
413C2×Q8—41no—
414C2×Q8C22⋊C4×C12712yes—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—21no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4C22⋊C4×C12712yes—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—24no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—81no—
456C22×C4—81no—
457C22×C4C22⋊C4×C12712yes—
458C22×C4C22⋊C4×C12712yes—
459C22×C4C22×C4×C12711yescharacteristic
460C22×C4C2×D4×C12711yescharacteristic
461C22×C4C2×D4×C12711yescharacteristic
462C22×C4C2×D4×C12711yescharacteristic
463C22×C4C2×D4×C12711yescharacteristic
464C22×C4C2×D4×C12711yescharacteristic
465C2×C8—41no—
466C2×C8—41no—
467C2×C8—41no—
468C2×C8—41no—
469C2×C8—41no—
470C2×C8—41no—
471C4⋊C4—24no—
472C4⋊C4—24no—
473C4⋊C4—24no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4C22⋊C4×C12712yes—
487C4⋊C4C22⋊C4×C12712yes—
488C22⋊C4—24no—
489C22⋊C4—24no—
490C22⋊C4—24no—
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C42—24no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—22no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23C2×C22⋊C4×C12711yescharacteristic
508C23#120×C12711yescharacteristic
509C23#120×C12711yescharacteristic
510C23#135×C12711yescharacteristic
511C23#135×C12711yescharacteristic
512C23AGL(1,ℤ/8)×C12711yescharacteristic
513C23#137×C12711yescharacteristic
514Q8—42no—
515Q8—81no—
516D4—42no—
517D4—42no—
518D4—42no—
519D4—42no—
520D4—42no—
521D4—81no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—81no—
557C2×C4—84no—
558C2×C4—81no—
559C2×C4—81no—
560C2×C4—81no—
561C2×C4—81no—
562C2×C4—81no—
563C2×C4—81no—
564C2×C4—81no—
565C2×C4—81no—
566C2×C4C2×C22⋊C4×C12711yescharacteristic
567C2×C4C2×C22⋊C4×C12711yescharacteristic
568C2×C4#120×C12711yescharacteristic
569C2×C4#120×C12711yescharacteristic
570C8—81no—
571C8—81no—
572C22—21no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22#379×C12711yescharacteristic
592C22#416×C12711yescharacteristic
593C22#417×C12711yescharacteristic
594C22#449×C12711yescharacteristic
595C22#449×C12711yescharacteristic
596C22#452×C12711yescharacteristic
597C22#452×C12711yescharacteristic
598C22#454×C12711yescharacteristic
599C22#456×C12711yescharacteristic
600C22B(4,𝔽2)×C12711yescharacteristic
601C22#458×C12711yescharacteristic
602C4—21no—
603C4—21no—
604C4—21no—
605C4—21no—
606C4—42no—
607C4—42no—
608C4—42no—
609C4—42no—
610C4—42no—
611C4—82no—
612C4—82no—
613C2—21no—
614C2—21no—
615C2—21no—
616C2—21no—
617C2—82no—
618C2C127×#159711yescharacteristic
619C2C127×#160311yescharacteristic
620C2C127×#160911yescharacteristic
621C2C127×#161511yescharacteristic
622C2C127×#178811yescharacteristic
623C2C127×#179011yescharacteristic
624C2C127×#179311yescharacteristic
subgroupG/H
center, socleC23×C127#120
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC2×#121×C127C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C23×C4×C127 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C127×#1872C2semidirect
4. C2×#328×C127C2semidirect
6. C2×#324×C127C2semidirect
7. C127×#1441C2semidirect
11. #539×C127C4semidirect
300. #8407C127direct (N × H)
315. #1872C2×C127semidirect
316. C2×#328C2×C127semidirect
318. C2×#324C2×C127semidirect
319. #1441C2×C127semidirect
320. C127#8407direct (N × H)
324. #539C4×C127semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#539×C1272
C127×#18742
C127×#18722
C2×#328×C1272
C2×#327×C1272
C2×#324×C1272
C127×#14412
#8407127